I think people are confusing Quicksort the partition-based sorting algorithm, and “qsort” the various library implementations. I prefer to see Quicksort the algorithm as having a pluggable pivot selection algorithm, which is quite essential in analyzing its behavior. If the first element is always chosen as the pivot, then an already sorted list is the … Read more
Picture an array: 3, 5, 2, 7, 6, 4, 2, 8, 8, 9, 0 A two partition Quick Sort would pick a value, say 4, and put every element greater than 4 on one side of the array and every element less than 4 on the other side. Like so: 3, 2, 0, 2, 4, … Read more
Make the graph bigger and you’ll see that O(n logn) isn’t quite a straight line. But yes, it is pretty near to linear behaviour. To see why, just take the logarithm of a few very large numbers. For example (base 10): log(1000000) = 6 log(1000000000) = 9 … So, to sort 1,000,000 numbers, an O(n … Read more
The Original Haskell Code There are two issues with the Haskell version: You’re using string IO, which builds linked lists of characters You’re using a non-quicksort that looks like quicksort. This program takes 18.7 seconds to run on my Intel Core2 2.5 GHz laptop. (GHC 7.4 using -O2) Daniel’s ByteString Version This is much improved, … Read more
One of the major factors is that quicksort has better locality of reference — the next thing to be accessed is usually close in memory to the thing you just looked at. By contrast, heapsort jumps around significantly more. Since things that are close together will likely be cached together, quicksort tends to be faster. … Read more
Radix sort is harder to generalize than most other sorting algorithms. It requires fixed size keys, and some standard way of breaking the keys into pieces. Thus it never finds its way into libraries.
Correct, the extra space are the log(n) stack frames. From the Wikipedia article of Quicksort: There is a more complex version which […] can achieve the complete sort using O(log n) space (not counting the input) on average (for the call stack). While you could implement quicksort iteratively (i.e., using a loop instead of recursion), … Read more
Quick sort works well for sorting in-place. In particular, most of the operations can be defined in terms of swapping pairs of elements in an array. To do that, however, you normally “walk” through the array with two pointers (or indexes, etc.) One starts at the beginning of the array and the other at the … Read more
Two arguments come to my mind: Quicksort/Introsort is more flexible: Quicksort and Introsort work well with all kinds of data. All you need for sorting is the possibility to compare items. This is trivial with numbers but you can sort other data as well. Radix sort on the other hand just sorts things by their … Read more
Complexity A Quicksort starts by partitioning the input into two chunks: it chooses a “pivot” value, and partitions the input into those less than the pivot value and those larger than the pivot value (and, of course, any equal to the pivot value have go into one or the other, of course, but for a … Read more